Fusome topology and inheritance during insect gametogenesis

From insects to mammals, oocytes and sperm develop within germline cysts comprising cells connected by intercellular bridges (ICBs). In numerous insects, formation of the cyst is accompanied by growth of the fusome—a membranous organelle that permeates the cyst. Fusome composition and function are best understood in Drosophila melanogaster: during oogenesis, the fusome dictates cyst topology and size and facilitates oocyte selection, while during spermatogenesis, the fusome synchronizes the cyst’s response to DNA damage. Despite its distinct and sex-specific roles during insect gametogenesis, elucidating fusome growth and inheritance in females and its structure and connectivity in males has remained challenging. Here, we take advantage of advances in three-dimensional (3D) confocal microscopy and computational image processing tools to reconstruct the topology, growth, and distribution of the fusome in both sexes. In females, our experimental findings inform a theoretical model for fusome assembly and inheritance and suggest that oocyte selection proceeds through an ‘equivalency with a bias’ mechanism. In males, we find that cell divisions can deviate from the maximally branched pattern observed in females, leading to greater topological variability. Our work consolidates existing disjointed experimental observations and contributes a readily generalizable computational approach for quantitative studies of gametogenesis within and across species.

Drosophila has emerged as a powerful experimental model for studies of germline cyst formation, cell cycle regulation, and robust cell fate specification [17,[23][24][25][26]. In Drosophila, sperm and oocytes develop within germline cysts that invariantly comprise 16 cells. To form the cyst, a founder cell-gonialblast in males, cystoblast in females-undergoes several divisions to form a 16-cell cyst, which ultimately gives rise to 64 spermatids in males, and a single oocyte in females (Fig 1A). A prominent feature of the developing germline cyst in Drosophila and numerous other insects is the fusome [5,9,10,17,[27][28][29]]-a membranous organelle that grows with each cell division during cyst formation, giving rise to a finger-like backbone that permeates the germline cyst through the ICBs (ring canals in Drosophila) [17,30,31]. The fusome is rich in vesicular and fibrillar structures and comprises several cytoskeletal proteins such as α-and β-Spectrin, the adaptor Ankyrin, the adducin-like protein, Hu-li tai shao (Hts), and the spectraplakin Short stop (Shot) [17,27,[31][32][33][34].
The fusome plays important but different roles in gametogenesis in males and females. In females, the germline cyst forms a highly invariant and maximally branched 16-cell tree ( Fig  1B), which arises from a founding cystoblast that undergoes four rounds of synchronous and incomplete divisions [21,25,35]. The fusome arises from a precursor called the spectrosome that is found in the cystoblast [25,36]. At each cell division in the 2-, 4-, and 8-cell cyst, fusome material is anchored at one end of the mitotic spindle, thus orienting the planes of cell division and ensuring the stereotypical branched pattern of the germline cyst (Fig 1A and 1C) [17,34]. In addition, the fusome has also been shown to link membranes of endoplasmic reticulum between all cells in a developing cyst, further enhancing cell-cell communication and assisting mitotic synchrony during the series of divisions [37]. The topology of the fusome therefore reflects and dictates the topology and connectivity of the germline cyst. However, it remains unclear when or how this cell network becomes polarized. Intercellular differences in fusome material have been implicated in symmetry breaking within the female germline cyst at the very first cell division. Here, asymmetry in fusome inheritance during germline cyst formation has been proposed to drive the specification of an oocyte through preferential microtubuledependent transport of oocyte fate determinants to the cell with the greatest amount of fusome [8,17,19,20,[38][39][40]. Alternatively, cyst asymmetry could arise later, such as in the completed 16-cell cyst. In this case, the fusome may not drive cyst polarization, but reflect an underlying asymmetry established by some mechanism that does not necessarily involve the fusome itself. However, despite the fusome's central role during oogenesis, the dynamics of fusome growth and its inheritance within the growing germline cyst have not been quantified.
In males, where all cells are equivalent and give rise to 64 spermatids through two additional meiotic divisions [4,19,21], the fusome also plays a part [21,[41][42][43]. Here, the fusome is thought to be dispensable under normal conditions [19]; however, in cases of DNA damage, the fusome facilitates synchronization of spermatogonial death, thereby shielding the integrity of gamete genomes [20]. Formation and growth of the fusome during spermatogenesis is thought to occur through a similar sequence of divisions as in oogenesis, where synchronous divisions of a gonialblast are accompanied by concomitant growth of the fusome, leading to a maximally branched CLT. However, fusome topology within male cysts and its effects on cyst A founder cell gives rise to a germline cyst whose 16 cells are connected through ICBs or ring canals. During oogenesis, one cell becomes the oocyte while the remaining cells serve a supporting role. During spermatogenesis, two subsequent meiotic divisions with incomplete cytokinesis generate 64 haploid spermatids. In both sexes, germline cysts contain a fusome, which permeates the cysts through the ring canals. B) Schematic of the four rounds of synchronous cell divisions that give rise to the female germline cyst, comprising 16 cells (nodes) connected by 15 ring canals (edges). The fusome (cyan) derives from the spectrosome and grows with each cell division; association of the fusome with one of the two mitotic centrosomes orients the planes of cell division, ensuring the stereotypical and maximally branched pattern in female cysts. C) Projection of a 3D image showing the fusome (α-Spectrin, Spec) permeating the cyst through the ring canals (Pavarotti, Pav) in cysts of various sizes (2-, 4-,8-and 16-cell cysts, and a Stage 1 egg chamber (EC)). Scale bar = 5 μm. D) Schematic for the 'predetermination' model for oocyte selection, which posits that the initial bias in fusome volume determines which cell becomes the oocyte; as such, oocyte identity is determined at the 1-cell stage. E) Projection of a 3D image of developing cysts during spermatogenesis, where the fusome (Adducin) and ring canals (Pav) are shown. Scale bar = 20 μm. F) Schematic showing that cell divisions can occur in one of two ways based on the orientation that the internal cells (green) divide. If all internal cells divide to form new branches, the cyst will remain maximally branched; however, internal cells can also divide without forming new branches, thus creating in-line divisions and paving the way for topologies that deviate from the maximally branched pattern.
topology are less understood than in females and have yet to be confirmed through direct reconstructions.
To address these gaps in knowledge, we leveraged advances in high resolution confocal microscopy and a recently developed and tested pipeline for 3D image analysis and quantification [44] to measure and reconstruct the fusome and its growth dynamics at all stages of cyst formation in both sexes (Fig 2). In females, we show that cystoblast divisions are not inherently asymmetric with respect to fusome partitioning and that, instead, newly generated fusome fragments are shared equally between mother and daughter at each division-as predicted by a minimal mathematical model of additive fusome growth. In males, we demonstrate a greater diversity of germline cyst topology than previously appreciated, and reconcile these findings with the divergent functions of the fusome in both sexes. The algorithm developed here can be readily extended to any experimental system comprising cells connected via ICBs, such as those that arise during animal gametogenesis [1][2][3][4][5][6][7][8][9][10][11][12][13]. Our work thus contributes a valuable computational tool that can recover key morphological features of germline cyst development, permitting comparative studies of gametogenesis within and across species.

Supervised learning for network topology reconstruction
To analyze fusome topology and intercellular volume distribution during cyst formation in females, we implemented a supervised learning algorithm to identify the location of fluorescently-labeled fusome and ring canals within the developing cyst (Fig 2)-as previously described [44,45]. Briefly, for each cyst, the fusome (fluorescently-labeled through tagging of α-Spectrin in females and adducin in males) and the ring canals (through endogenouslytagged Pavarotti, a key component of ring canals in Drosophila) were identified using the supervised learning program ilastik [45,46], which has been used in several other settings for volumetric reconstructions of cells and subcellular structures [44,[47][48][49]. Although the marker for fusome between the males and females was different, both of these have been demonstrated to be reliable markers of fusome size and shape [31,36]. The fusome in females was taken as a single, simply-connected component within the developing germline cyst. Ring canals did not have this constraint, and based on the sample under consideration, either 1, 3, 7, or 15 rings were required to complete the fusome segmentation and reconstruction upon using skeletonization to identify objects which were closed loops within each image stack (corresponding to 2-, 4-, 8-, and 16-cell cysts, respectively). Each ring canal, which necessarily surrounds the fusome at cell junctions, was used as a marker to splice the fusome into multiple sections. A recursive function was then built so that for each distinct ring canal, the fusome was split into two fragments on either side.
At the first iteration, the fusome was split into two fragments. The algorithm then iteratively split the fusome at each ring canal, generating fragments that corresponded to the volumes present within each cell of the cyst. After generating these fragments, the function then logged information about their volumes and positions within the stack and moved to a different branch of the recursive loop. The final output of this algorithm was a three-dimensional stack of separated fusome fragments, whose sum amassed the entirety of the original fusome. These objects were then exported for further identification based on mutual adjacencies to assign a unique label to each piece of fusome based on its number of neighbors and distance from the presumed founder cell (in females). The volume of each fragment was calculated based on the number of voxels within each object, multiplied by the known voxel size.
We found that our pipeline reconstructed the correct maximally branched cyst structure in females (Fig 2A). Because the topology of the network at each division is symmetric during  [44,45] produced a 3D reconstruction of the fusome and ring canal system at successive stages of germline cyst formation ( Fig 1A). From here, ring canals at the junction between sister cells were used to segment the fusome into its component parts (multicolored cells) and, in the case of oogenesis, produce an adjacency matrix representing intercellular connections within the cyst to compare with the known female germline cyst network topology, permitting unambiguous cell label assignments to the individual fusome fragments. These fusome fragments were then labeled according to their position relative to the presumptive oocyte. (B) Male cysts underwent the same procedure of collective adjacency information, but as no oocyte is present, no distinction was made between cells. Scale bars = 2 μm (A) and 10 μm (B). https://doi.org/10.1371/journal.pcbi.1010875.g002

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Fusome topology and inheritance during insect gametogenesis oogenesis, the cell with the larger fusome fragment and four ring canals was labeled cell 1. Each cell thereafter was uniquely identified based on its number of neighbors and proximity (number of intervening ring canals) to cell 1.
From here, the volumes of fusome within each cell in the cyst were also recorded to enable intercellular comparisons in the dividing cyst. Manual validation of ilastik volumes was performed on a subset of randomly selected samples. For each sample, manual thresholding was performed in FIJI to identify fusome area at each slice. All slices were summed and the total was multiplied was the voxel size to yield a fusome volume estimate. Across all samples, the difference between manual and automated fusome volumes was � 8% on average (S1 Data).
To further test and extend the applicability of the developed algorithm, we turned our attention to the male, where we analyzed the 3D structure and topology of fusomes at successive stages of cyst formation ( Fig 2B) [44,45]. In contrast to the female cyst, where cells were tightly packed and the fusome compact, male germline cysts appeared more elongated, with threadlike fusomal materials connecting otherwise seemingly disjoint fusome fragments, as highlighted previously [19,38,43,50].

Quantifying fusome growth dynamics during oogenesis
Intercellular asymmetry in fusome distribution is thought to mediate oocyte fate specification and polarity, which in Drosophila ultimately establish the embryo's main body axes [17,25,26]. According to this 'predetermination' model for oocyte selection, the cell that contains the greatest amount of fusome becomes the oocyte, and that cell is always one of the two cells with four ring canals-the pro-oocytes ( Fig 1C). This model builds on the fact that asymmetry in fusome content arises during the very first cell division, and that this asymmetry between the first cell and remaining cyst cells, including the other pro-oocyte, is maintained during subsequent divisions [27,36,51]. As microtubules associate with the fusome, its asymmetry is proposed to predetermine oocyte identity by directing the microtubule network towards one cell, along which dynein transports oocyte fate determinants [25,30,52,53]. Formation of a polarized microtubule network is indeed key for oocyte specification [23,53]. For example, egalitarian, in concert with Bicaudal-D, promotes the microtubule-dependent transport of factors to the presumptive oocyte; its mutants form cysts with 16 nurse cells despite forming normal fusomes that appear asymmetrically distributed [54][55][56][57]. The alternative model for oocyte selection postulates that fusome asymmetry is insufficient for determining oocyte fate; instead, the pro-oocytes are considered equivalent, with both having an equal chance of becoming the oocyte [25,58]. According to this model, one of the pro-oocytes becomes the oocyte 'stochastically', through competition for some limiting oocyte determining factor(s) at the 16-cell stage ( Fig 1C).
Quantification of fusome growth, inheritance, and relative fusome volumes within connected cells is key for distinguishing between models; however, these measurements are technically challenging. A further complication is the fact that oocyte identity only becomes clear once the 16-cell cyst of Drosophila is formed-a point at which several fusome components have begun to disintegrate [25,30,58,59]. Here we take steps to address this gap using the supervised learning approach described above, limiting the analysis to cysts lying within the germarium and with fully intact fusomes. Flies heterozygous for an orb null mutation (orb is a known oocyte-specifying factor) were dissected for this analysis. Previous work did not identify any abnormalities in fusome formation, cyst formation, or cyst progression through the germarium in these samples [60]; our own analysis confirmed that these early stages of oogenesis were not affected.
Our data revealed a strong bias in fusome volumes between the pro-oocytes starting at the 2-cell stage. Specifically, our results showed that, for 2-cell cysts, the larger of the two fusome fragments comprised, on average, 70% of the total fusome volume. Subsequent divisions, however, decreased the asymmetry between the two most central cells, with the ratio of volumes between cells 1 and 2 decreasing from 2.4 ± 0.3 in the 2-cell cyst (n = 12) to 1.2 ± 0.2 in the 16-cell cyst (n = 11) (Fig 3). Nonetheless, at each stage, there was a persistent fusome volume bias toward these two central cells compared to the other 14: upon successive divisions to form a 4-, 8-, and finally 16-cell cyst, the volume fraction of these two cells was 78 ± 7% (n = 12), 58 ± 6% (n = 6), and 37 ± 3% (n = 11), respectively, dwarfing the fusome portions in each other cell at every stage of division.
We also found that aggregating the volume fractions based on ring canal number provided a meaningful metric with respect to when each cell is formed in the successive divisions. In particular, we found that cells with 4, 3, 2, and 1 ring canals comprised 37 ± 3%, 21 ± 3%, 22 ± 2% and 20 ± 3% of the total fusome volume (n = 11), respectively. Note that the two cells with 4 ring canals are the pro-oocytes. Within the measurement error of each group and for comparison with theory, these groupwise fractions at the 16-cell stage are taken as the following ratio: 2 : 1 : 1 : 1.
To rationalize these experimental data, we developed a minimal theoretical framework to model how relative fusome volume fraction in each cell changes during cyst generation. This model was built on the fact that the fusome in Drosophila grows through successive rounds of accumulation and fusion of fusome fragments in the ring canals connecting mother and daughter cells [25,51,58,59]. Here, we only assumed that at each division there was no additional change in the relative volume fractions of fusome in the cells between divisions, other than what was added from the fusome plug [25,51]. This model therefore treated the fusome as an irreducible building block, where plugs chain together at each division to form a larger and branched structure.
Building on these assumptions, we wrote a series of equations with two parameters: α, the volume fraction of fusome in the founder cell at the 2-cell stage, and β, the fraction of the fusome plug added to the parent cell at each division (see Materials and Methods). Using the 2 : 1 : 1 : 1 heuristic for the groupwise fractions at the 16-cell stage and inserting the derived relationships into equations for the volume fractions for each cell in the 2-, 4-, 8-, and 16-cell cysts yielded volume fractions that enabled direct comparison of model predictions with experimental measurements over a range of values for α and β (Fig 3D). For the parameter range α 2 [0.25, 0.75] and β 2 [0.25, 0.75], we found α = 0.700 and β = 0.515 minimized the error with our measurements, yielding for a range of values for α and β. Considering the range of parameters that yielded errors within 5% of the minimum gave ranges of α 2 (0.688, 0.705) and β 2 (0.480, 0.559). Notably, this interval for β captured the value 0.5, suggesting that fusome fragments are shared equally upon division [25,51].

Reconstructing fusome and cyst topology during spermatogenesis
In any interconnected cyst, two types of cells exist: terminal cells-the cells at the very ends of the cyst, connected to only one other cell-and internal cells. Upon division, terminal cells form one cell connected to two cells and another cell that now again has only one connection (Fig 1F). In other words, terminal cell divisions results in an internal cell and a terminal cell. On the other hand, internal cells can divide in two ways: they can form a new terminal cell or two internal cells. These division types affect CLT topology: maximally branched trees form when all internal cells divide to form terminal cells ( Fig 1F); however, if in-line divisions occur, maximal branching is lost. By tracking cell-cell connections, the topology of the germline CLT can be extracted [61,62]. With these division rules in mind, we set out to catalog the series of connections present in male germline cysts and to compare those to the known sequence of divisions during Drosophila oogenesis.
Reconstructions of fusomes in male cysts revealed significant fusome fragmentation ( Fig  4A). Indeed, we found that in only (50%) of reconstructed samples was the number of fusomeconnected cells 2 n , in contrast to females, where in all samples the number of fusome-connected cell was 2 n . This deviation in males is unlikely to be due to an atypical number of cells. Indeed, when we counted the spermatid tails per sperm tail bundle present across a number of post-meiotic cysts, we observed an average of 63.1 ± 1.3 (n = 61) spermatids per bundle, consistent with each cyst comprising 16 cells (S2 Data) [63,64]. To explore the effects of fusome fragmentation, we analyzed the various topologies that could be recapitulated by tracing fusomal connections in males, assuming that fusome topology reflects that of the CLT. Starting from a single cell, there is only one path towards forming a four-cell cyst via synchronous divisions: a linear fusome fragment with three ICBs. Upon dividing synchronously again, multiple eight-cell cysts are possible, depending on whether the divisions occur in a maximally

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Fusome topology and inheritance during insect gametogenesis branched fashion; that is, whether or not each division forms a new terminal fusome fragment budded off from the parent (Fig 1F). For cells at the terminal ends of the cyst, the fusome can only elongate in one manner; however, for the inner cells, the fusome either adds a branch or continues growth in a linear manner. By symmetry, one is left with three possible configurations for the cyst; of these, only one configuration is maximally branched, whereby each division creates a new branch (Fig 1F). Of all fusome reconstructions encompassing 5-8 cells (n = 21), we found none that were inconsistent with the maximally branched connections of an 8-cell cyst (Fig 4A).
Starting with maximally branched 8-cell cysts then, 36 possible configurations are obtainable through another division to form a 16-cell cyst, with only one resulting in a maximally branched network. We analyzed fusome reconstructions connecting 9-16 cells and, while we observed fusomes whose structure was consistent with a 16-cell maximally branched cyst, we uncovered fusomes whose connections could not be embedded onto a maximally branched topology. Even in cases where fusomes did not connect 16 cells, the topology of the largest fragment was sufficient to demonstrate that divisions had not occurred in a maximally branched manner (Fig 4B). We next analyzed the orientation of mitotic spindles in dividing cysts, focusing on the fourth division cycle, when the cyst increases in cell number from 8 to 16. In female cysts, mitotic spindles align such that newly-formed cells divide to create a maximally branched tree as opposed to 'in-line' (Fig 1B); the fusome follows cyst growth, leading to its branching throughout the cyst [17]. This division pattern was observed in all dividing 2and 4-male cysts, but not in 8-cell cysts, where we found mitotic spindles that were parallel to two disjoint fusomal fragments (Fig 4C)-consistent with cell division elongating the fusome rather than giving rise to a new branch. These findings suggest that the stereotyped pattern of connections in female cysts are not strictly preserved during spermatogenesis and that deviations from maximally branched structures in male cysts arise at the fourth division during cyst formation.

Discussion
The fusome has long been identified as a prominent feature of developing germline cysts in insects; first described in spermatocytes more than a century ago, the fusome has since been observed in numerous species [5,9,10,17,[27][28][29]. Fusome composition and function are best described in Drosophila [17,25,27,30,32,35,36,51], yet questions remain regarding its growth and inheritance pattern in females, as well as its topology in males. Here we set out to address these gaps in knowledge by adapting a machine-learning approach for 3D reconstructions of cells and their substructures [44].
In females, the nonuniform distribution of the fusome has been implicated in oocyte selection [17,30]. The 'predetermination' model for oocyte selection posits that the slight asymmetry provided by the fusome biases the choice of oocyte to the first cell-a fate that is then sealed by directing flow of other determinants [34][35][36]51]; the alternative 'stochastic' model for oocyte selection suggests that pro-oocytes are equivalent, but does not account for how oocyte selection is restricted to those two cells [24,58,65].
Based on direct measurements of fusome volumes in daughter cells at successive stages of germline cyst formation, we show that cystoblast divisions are not asymmetric with respect to fusome partitioning; instead, our data are consistent with a model in which newly generated fusome fragments are shared equally between mother and daughter at each division and where the fusome is assembled in an additive manner. Asymmetry in fusome distribution in the cyst therefore arises by propagating the advantage that the founding cystoblast has by virtue of containing the spectrosome. Consequently, fusome asymmetry between the pro-oocytes decreases with each cell division, while asymmetry between the pro-oocytes and the rest of the cyst increases as the volume fraction of these two cells dwarfs that in all other cells in the cyst. Note that while these analyses were performed on germline cysts heterozygous for a mutation that disrupts expression of the oocyte-specifying factor orb, we did not observe any abnormalities in the formation of the fusome, nor in the divisions of the germline cyst and its progression throughout the germarium, in agreement with previous work [60]. Future work should consider data from wild type animals; nonetheless, we expect the aforementioned results to hold.
Given these data, the strict dichotomy between the two oocyte selection models ('stochastic' versus 'predetermined') is potentially overstated; further, neither model is consistent with all previous experimental observations of mutants in which oocyte selection is inhibited [58], delayed [66], or where multiple oocytes are specified [67,68]. Instead, we propose a third model of 'equivalency with a bias', whereby the amplified fusome asymmetry between the prooocytes and the remaining cells biases the choice of oocyte to the two pro-oocytes, while the decreasing fusome asymmetry between the two pro-oocytes themselves means that which of the pro-oocytes is chosen as the oocyte at the 16-cell stage is likely to be stochastic. Such a twostep mechanism, one that relies on the interplay of predetermined factors to limit the pool of candidates and stochastic factors for the final selection has been documented in other wellstudied systems of robust cell fate determination, such as the invariant spatial patterning of the equipotent vulval precursor cells in C. elegans and the achaete(ac)-scute(sc) system in bristle determination in the adult Drosophila cuticle [69][70][71][72]. Testing the validity of this 'equivalency with a bias' model will require analyses correlating fusome volume of the pro-oocytes with concentrations of orb and/or other oocyte-selecting factors at the 16-cell stage during cyst formation. Here, a strong correlation between relative fusome volume and preferential localization of an oocyte-selecting factor in one of the pro-oocytes would support the predetermination model; the alternative scenario, whereby there is a weak or no correlation between these measurements at the 16-cell stage would suggest that the pro-oocytes are equivalent in their potential to become oocytes, and that ultimate oocyte selection is stochastic and is not determined by differences in fusome volume between the pro-oocytes.
In males, the fusome is also a prominent structure, and while it is thought to be unimportant for normal development [19], it appears to play a crucial role in mediating intercellular connectivity and synchronized cell behaviors under stress [20]. Male fusomes also last longer: while fusomes start to disintegrate following formation of the 16-cell cyst in females, male fusomes persist following meiosis [40]. Despite these inherent differences, the topology of the male fusome, and consequently that of the germline cyst, have long been assumed to mirror those of female maximally branched structures. By analyzing fusomes at successive stages of cyst development, we instead found that division orientation in male cysts exhibits greater variability those in females, particularly where the fusome has become thread-like or fragmented.
To our knowledge, our computationally-derived 3D reconstructions of the fusome-ring system within the male germline cyst presented here are novel; however, we are not the first to demonstrate that male cysts may exhibit 'atypical' division patterns. A manual reconstruction by Rasmussen almost fifty years ago demonstrated that cell-cell connections in males did not align with the known maximally-branched pattern of female cysts [42]. The reconstruction and observations made by Rasmussen have since been largely lost to the field, with some authors later stating that "the distribution of ring canals among the cells of the cyst appears to be the same as described by King for oogenesis. . .; the recent report to the contrary by Rasmussen probably represents an exceptional cyst." [73].
Rasmussen concluded that the observed atypical male cyst must have formed as the result of five mitotic divisions [42]. Alternatively, as our results suggest here, cysts without a maximally branched structure can arise through four synchronous mitotic divisions, where the final divisions occur without maximal branching (Fig 4B). Consequently, the number of ring canals connecting a cell in the developing male cyst is not a strict indicator of the age of the cell as is the case in female cysts, where cells divide with maximal branching only. These findings can be interpreted in the context of the divergent outcomes of gametogenesis in both sexes: a cyst whose cells all share the same fate in males, and a cyst that produces a single oocyte in females through the directed transport of materials by the other 15 supporting nurse cells. Compared to females, males may therefore have less stringent requirements for setting up a polarized microtubule transport network that would require an intact fusomal backbone that is asymmetrically partitioned within the cyst.
Reconstructions of germline cysts in various species have revealed a slew of diverse topologies, from linear chains in the plumed worm to star-like cysts in the white worm where cells connect to a central cytophore [1,18,74,75]. Recent studies have also revealed the presence of ICBs in choanoflagellates-a model organism for studies of the origins of multicellularity [44,76]. While the results here are derived based on the known division patterns during Drosophila oogenesis, the developed analysis pipeline is readily generalizable to any species whose germline cysts develop with the aide of fusomal material, such as those of the order Lepidoptera [77,78] and those that do not, like the mouse [79]. The approach presented here will therefore be key for expanding the zoology of cyst structures in the animal kingdom and for investigating the interactions between cyst structure and size, and how these vary within and across species [18,80,81].

Fly stocks and sample preparation
Pav-mCherry females heterozygous for the orb null mutation orb F343 (gift from Schedl lab, Princeton University) were used in this study as a marker for ring canals and to allow for isolation of 16-cell cysts. Ovaries were dissected and fixed as previously described, taking care to isolate germaria from ovarioles [44,82]. After blocking, the primary antibody mouse anti-α-Spectrin 3A9 (1:30, gift from Schedl lab, Princeton University) was added and rocked overnight at 4˚C overnight. The secondary antibody rat anti-mouse Alexa-Fluor 488 (1:100, Invitrogen) was then added to mark the fusome within each 2-, 4-, 8-, and 16-cell cyst in the germaria. Dissected ovaries were mounted in a 75:25 mixture of RapiClear 1.47 (SUNJin Lab) and Aqua-Poly/Mount (Polysciences).
Ubi-Pavarotti-GFP male flies (gift from Glover lab, California Institute of Technology) were dissected according to standard protocols [46]. Immunofluorescence staining was performed as described previously [83]. Briefly, tissues were dissected in PBS, transferred to 4% formaldehyde in PBS and fixed for 30 minutes. Tissues were then washed at least three times for 10 minutes in PBS-T (PBS containing 0.1% Triton X-100), followed by incubation with primary antibody in 3% bovine serum albumin (BSA) in PBS-T at 4˚C overnight. Samples were then washed three times for 20 minutes in PBS-T, incubated with secondary antibody in 3% BSA in PBS-T at 4˚C overnight, washed as above, and mounted in Vectashield with DAPI (Vector Labs). The following primary antibodies were used: rabbit anti-Phospho H3 (Ser10) (1:200, Thermo Fisher) and mouse anti-Hts (1:20, 1B1, Developmental Studies Hybridoma Bank). Secondary antibodies used were anti-rabbit IgG Alexa Fluor 488 and anti-mouse IgG Alexa Fluor 647 (both 1:200). Fluorescent images were acquired using a Leica TCS SP5 confocal microscope with a 63x/1.3 NA oil objective.
Confocal imaging was performed on a Leica SP5 confocal microscope using a 63x/1.3 NA oil objective. Three dimensional stacks were acquired using 488 and 546 nm lasers in series over roughly 100 slices of 16-bit, 1024 x 1024 images. Voxel sizes of acquired images were roughly 70 nm in x and y, and 210 nm in z.

Spermatid tail preparation and imaging
Testes were fixed for 1 hour or overnight (at 4˚C) with 2.5% glutaraldehyde in 0.1M Sorensen's buffer, pH 7.4. Samples were rinsed twice for 5 minutes each with 0.1 M Sorensen's buffer and post-fixed for 1 hour in 1% osmium tetroxide in 0.1 M Sorensen's buffer. Next, testes were rinsed twice in double distilled water for 5 minutes each and en bloc stained with 2% uranyl acetate in double distilled water for 1 hour. The samples were then dehydrated in increasing concentrations of ethanol, rinsed with acetone, and embedded in epon epoxy resin. Thin sections were mounted on Formvar/carbon-coated slotted grids and post-stained with uranyl acetate and lead citrate. Samples were examined on a JEOL1400 transmission electron microscope and images captured using a sCMOS XR401 custom-engineered optic camera by AMT (Advanced Microscopy Techniques).

Image acquisition and processing
Raw image stacks were first pre-processed to isolate individual cysts. Within germaria, intact fusomes were taken at the 2-,4-,8-, or 16-cell stage, provided the fusome was still fully connected throughout the cyst. Because male cysts maintain their fusome until the formation of 64 cells, only samples near the apical tip of the testis containing up to 16-cells based on counting nuclei near fusome pieces were taken [19]. Stacks were uploaded into ilastik for Pixel Classification to identify the locations of fusome and ring canals for each sample, in a manner similar to previous work [44,45]. For each type of data, training was performed by manually identifying pixels that belong to each class of interest. This positional information, a set of probabilities at each voxel for belonging to fusome, ring, or image background, were imported into MATLAB for object identification and volume measurement. Using the probabilities for each voxel to be part of the fusome and ring canals, simple thresholding was used to find the most likely positions for each class.
Due to the invariance of cyst structure in the Drosophila female germline, the adjacencies between cells in the female cyst were known up to the identification of one cell due to cyst symmetry. In this case, larger fusome fragment with the most ring canals were taken to be the founder cell (cell 1), making it possible to assign all other identities within each cyst. The adjacencies for each set of fusome fragments were identified and mapped to the known adjacency matrices at each cyst size, allowing for reassignment through the Hungarian algorithm as previously described [44,84].
In males, fusome fragmentation required manual segmentation and validation to ensure proper cell-cell adjacencies were collected. Samples stained with Phospho H3 were additionally trained within ilastik and inserted into MATLAB for further analysis for positioning. 3D reconstructions allowed for the identification of cells dividing without the formation of new fusome branches.

Mathematical model for fusome assembly in females
In this section, we introduce a theoretical model for fusome formation during Drosophila oogenesis using known biological features of the process, accompanied by a small number of assumptions. This minimal model, in coordination with the measured fusome volumes across stages, seeks a more coarse-grained, less stochastic view of fusome formation during oogenesis.
It was previously shown that the cystoblast contains the spectrosome, a fusomal precursor [25,36]. Therefore, if the volume of the spectrosome in the cystoblast after division to form the 2-cell cyst is given by v 0 and the fusome volume added at the first division is v 1 , the volume fraction of cell 1 in the 2-cell cyst (f 1,2 ) is described by: where α is defined as the volume fraction of fusome in cell 1 after the first division and β is defined as the fraction of the fusome volume added to the already existing cell at each division ( Fig 3A). Extending this quantitative description to the next division, from a 2-cell to 4-cell cyst, we have two fusome plugs to add, each contributing v 2 to the total fusome volume ( Fig  3B). Under the assumption that fusome plugs added at each division are the same (in this case, v 2 ), the volume fractions in the cells of the cyst, f i,4 , can be derived: These derivations can be repeated at each subsequent division, allowing for fusome volume fractions in each cell of any cyst size to be defined (Fig 3A-C).
Our experimental measurements revealed that the average volume fractions of cells 1 and 2, cells 3 and 4, cells 5 through 8, and cells 9 through 16 at the 16-cell stage are given in the ratio 2 : 1 : 1 : 1. One can therefore write the following equations for the volume fractions of these groups of cells and, along with Eq 1, solve for v 1 , v 2 , v 3 , and v 4 , the average volume of the fusome fragment being added between mother and daughter at each division, in terms of v 0 : 4 ; ð7Þ 4 : ð8Þ Solving this system of equations, along with Eq 1, allows for one to solve for v 1 , v 2 , v 3 , and v 4 in terms of v 0 . Inserting the derived relationships into equations for the volume fractions for each cell in the 2-, 4-, 8-, and 16-cell cysts yields volume fractions that can be compared with experimental measurements at the parameter values α = 0.7 and β = 0.5 heuristic values close to the parameter values found to minimize the total error, as shown above (Fig 3D and S1 Fig).